%%% Section 3: Arithmetic Expressions %%%

exp(ePlus(E1, E2)) :- exp(E1), exp(E2).
exp(eTimes(E1, E2)) :- exp(E1), exp(E2).
exp(eInt(N)) :- integer(N).


token(tLparen).
token(tRparen).
token(tPlus).
token(tTimes).
token(tInt(N)) :- integer(N).


%% some very simple test cases

:- initialization(parse([tInt(1), tPlus, tInt(2), tTimes, tInt(3)],
                        ePlus(eInt(1), eTimes(eInt(2), eInt(3))))).

:- initialization(parse([tInt(1), tTimes, tInt(2), tPlus, tInt(3)],
                        ePlus(eTimes(eInt(1), eInt(2)), eInt(3)))).

:- initialization(parse([tLparen, tInt(1), tRparen], eInt(1))).
:- initialization(parse([tLparen, tInt(1), tPlus, tInt(2), tRparen],
                        ePlus(eInt(1), eInt(2)))).

:- initialization(parse([tLparen,tInt(1),tPlus,tInt(2),tRparen,tTimes,tInt(3)],
                        eTimes(ePlus(eInt(1), eInt(2)), eInt(3)))).

:- initialization(parse([tInt(1),tTimes,tLparen,tInt(2),tPlus,tInt(3),tRparen],
                        eTimes(eInt(1), ePlus(eInt(2), eInt(3))))).

% some negative examples if you decide to attempt the extra credit
%:- initialization(\+ parse([tPlus, tInt(1), tInt(2)], _)).
%:- initialization(\+ parse([tInt(1), tInt(2), tPlus], _)).
%:- initialization(\+ parse([tLparen, tRparen], _)).